Rate upper bound and optimal number of weight vectors for opportunistic beamforming

In opportunistic beamforming, the throughput can be improved by broadcasting multiple weight vectors in one time slot and selecting the best one. However, broadcasting too many weight vectors will consume the time for data transmission and thus bring down the throughput. In this paper, we investigate two multiple weight vector(MWV) opportunistic beamforming schemes tailored for fast fading and slow fading scenarios respectively and we derive tight upper bounds of the data rates for both schemes. To maximize the upper bounds, we obtain the optimal numbers of weight vectors to be broadcast. Simulation results demonstrate the validity of our theoretical analysis. Based on these results, we obtain some basic guidelines for MWV design problem. For the MWV scheme of fast Rayleigh fading scenario, we claim that (1) the faster the fading is, the less weight vectors are desired; (2) the more users there are, the less weight vectors are desired. For the MWV scheme of slow Rayleigh fading scenario, we have the conclusion that a small number of weight vectors are good enough to achieve a desirable performance.